The process of "second harmonic generation" (SHG) is one of a number of non-linear optical (NLO) processes (e.g., difference-frequency generation, sum-frequency generation, optical mixing, parametric oscillation, etc.) by which light at one wavelength is converted into light of another wavelength. Specifically, in a SHG process, light at a fundamental wavelength (i.e., angular frequency .omega.) is converted to light having a wavelength of one half (i.e., 2.omega.) of the fundamental (e.g., the second harmonic). Thus, using an appropriate NLO material, two photons can be added together in a SHG process to result in a single photon of higher energy. Second harmonic generation has been reviewed by A. Yariv in Quantum Electronics, 2nd Ed., John Wiley & Sons, New York, 1975, pp. 407-434 and by W. Koechner in Solid State Laser Engineering, Springer-Verlag, N.Y., 1976, pp. 491-524.
Materials having non-linear optical properties are well known. For example, U.S. Pat. No. 3,949,323, issued to Bierlein et al. on Apr. 6, 1976, discloses that non-linear optical properties are possessed by materials having the formula MTiO (XO.sub.4) where "M" is at least one of K, Rb, Ti, or NH.sub.4 and "X" is at least one of P or As, except when NH.sub.4 is present, then "X" is only P. This generic formula includes potassium titanyl phosphate, KTiOPO.sub.4, or KTP, which is a particularly useful non-linear material. Other known non-linear optical materials include, but are not limited to, KH.sub.2 PO.sub.4 or KDP, LiNbO.sub.3, KNbO.sub.3, .beta.-BaB.sub.2 O.sub.4, Ba.sub.2 NaNb.sub.5 O.sub.15, LilO.sub.3, HlO.sub.3, KB.sub.5 O.sub.8 4H.sub.2 O, potassium lithium niobate and urea. A review of the non-linear optical properties of a number of different uniaxial crystals has been published in Sov. J. Quantum Electron., Vol. 7, No. 1, January 1977, pp. 1-13. Non-linear optical materials have also been reviewed by s. Singh in the CRC Handbook of Laser Science and Technology, Vol. III, M. J. Weber, Ed., CRC Press, Inc. Boca Raton, Fla., 1986, pp. 3-228.
Electromagnetic waves having a frequency in the optical range and propagating through a non-linear crystal induce polarization waves which have frequencies equal to the sum and difference of those of the exciting waves. Such a polarization wave can transfer energy to an electromagnetic wave of the same frequency. The efficiency of energy transfer from a polarization wave to the corresponding electromagnetic wave is a function of (a) the magnitude of the second order polarization tensor, since this tensor element determines the amplitude of the polarization wave; and (b) the distance over which the polarization wave and the incident electromagnetic wave can remain sufficiently in phase.
The coherence length, I.sub.c, is a measure of the phase relationship between the polarization wave and the incident electromagnetic wave and is given by the following relationship: EQU I.sub.c =.pi./.DELTA.k
where ".DELTA.k" is the difference or mismatch between the wave vectors of the polarization and incident electromagnetic waves. More specifically, the coherence length is the distance from the entrance surface of the non-linear optical crystal to the point at which the power of the radiated electromagnetic wave will be at its maximum value. "Phase-matching" occurs when .DELTA.k=0. The condition .DELTA.k=0 can also be expressed as n.sub.3 .omega..sub.3 =n.sub.1 .omega..sub.1 .+-.n.sub.2 .omega..sub.2 where .omega..sub.3 =.omega..sub.1 .+-..omega..sub.2 ; .omega..sub.1 and .omega..sub.2 are the frequencies of the input electromagnetic waves; .omega..sub.3 is the frequency of the radiated output electromagnetic wave; and and n.sub.1, n.sub.2 and n.sub.3 are the refractive indices of the respective waves in the non-linear optical crystal. In the special case of second harmonic generation, there is incident radiation of only one frequency, .omega.; therefore .omega..sub.1 =.omega..sub.2 =.omega. and .omega..sub.3 = 2.omega..
For appreciable conversion of optical radiation of one frequency to optical radiation of another frequency in a non-linear optical crystal, the interacting waves must stay substantially in phase throughout the crystal so that: EQU .vertline..DELTA.k.vertline.=.vertline.k.sub.3 -k.sub.1 -k.sub.2 .vertline.&lt;.pi./L
where k.sub.1, k.sub.2 and k.sub.3 represent the wave numbers corresponding to radiation of frequencies .omega..sub.1, .omega..sub.2, and .omega..sub.3, respectively, and "L" is the interaction length in the non-linear material. In the special case of second harmonic generation: ##EQU1##
The term "substantially phase-matched," as used herein, means that .vertline..DELTA.k.vertline.&lt;.pi./L for a given non-linear optical crystal.
A conventional method for achieving phase-matching in a non-linear optical material utilizes the fact that dispersion (i.e., the change of refractive index with frequency) can be offset by using the natural birefringence of uniaxial or biaxial crystals. In a typical case (Type I phase matched second harmonic generation) the fundamental and harmonic beams are orthogonally polarized in directions corresponding to the principal refractive indices of the crystal. The birefringence of the crystal is adjusted to compensate for the dispersion between the fundamental and harmonic radiation, thereby preserving the phase relationship between the two beams as they travel through the crystal. This technique, or modifications of it, can be used to achieve `true` phase matching of a number of different nonlinear interactions including sum and difference frequency mixing and second harmonic generation.
Engineering the optical properties of an existing material provides an alternative to materials in which true phase-matching can be achieved. Quasi phase-matching (QPM) compensates for refractive index dispersion in nonlinear optical interactions. Unlike techniques which utilize the birefringence of anisotropic materials, QPM can be applied to isotropic materials or to interactions in which the interacting waves have the same polarization. The doubling crystal can be tailored to phase-match any given wavelength at room temperature by setting the period of the alternating nonlinearity to be twice the anticipated coherence length.
Three methods of achieving quasi phase-matching have been described in "Interactions between Light Waves in a Non-linear Dielectric" by J. A. Armstrong et al., Physical Review, Vol. 127, pp. 1918-1919 Sep. 15, 1962).
Continuous power flow from the fundamental into its second harmonic can be maintained along the length of a crystal by changing (e.g., "periodic poling" or "domain reversal") the sign of the nonlinear coefficient of the material at odd multiples of the coherence length. For periodic poling, the crystal must be stable after the periodic structural changes are made. In addition, surface and crystal quality must be such that losses due to optical scattering and absorption are low. This is not always possible. Periodic poling has been used in conjunction with lithium niobate to generate green and blue light. See Magel et al., "Second harmonic generation of blue light in periodically poled lithium niobate", CLEO-89, paper ThQ3, and Lim et al., "Second harmonic generation of green light in a periodically poled lithium niobate waveguide", CLEO-89, paper ThQ4. Also see U.S. Pat. No. 4,731,787 to Fan et al (i.e., FIG. 3).
Another method involves total internal reflection of both the fundamental and harmonic waves in a crystal of thickness: EQU d=.pi. cos .THETA./.vertline.k.sub.2 -2k.sub.1 .vertline.
where "k.sub.2 -2k.sub.1 " is the wave vector mismatch, and ".THETA." is angle between the beam propagation direction and a normal to the crystal surface. This method has been used successfully to phase-match second harmonic generation of 10.6 .mu.m radiation in GaAs. See "Enhancement of Optical Second-Harmonic Generation (SHG) by Reflection Phase Matching in ZnS and GaAs," Boyd and Patel, Appl. Phys. Letters, 8, (1966) p. 313.
The final method, and the one to which the present invention is addressed, involves resonating the second harmonic in a crystal platelet which has a length L which is given by: ##EQU2## where .pi./.vertline.k.sub.2 -2k.sub.1 .vertline. is the coherence length for the interaction. Heretofore, this technique for achieving QPM does not appear to have been exploited by the art. In accordance with this method, if a monochromatic traveling wave is incident upon a "harmonic etalon" at a frequency which is one half that of one of its resonances, a harmonic wave is produced in the forward direction but not in the reverse.
Second harmonic generation within the cavity of a multi-longitudinal mode laser by an intercavity doubling crystal has been analyzed by T. Baer, J. Opt. Soc. Am. B, Vol. 3, No. 9, (1986) pp. 1175-1180. U.S. Pat. Nos. 4,656,635 and 4,701,929, both issued to Baer et al., disclose a laser diode-pumped, intracavity frequency-doubled, solid-state laser. A detailed theoretical analysis of a multi-longitudinal mode intracavity-doubled laser has been reported by X. G. Wu et al., J. Opt. Soc. Am. B, Vol. 4, No. 11, (1987) pp. 1870-1877.
In U.S. Pat. No. 4,847,851, G. J. Dixon disclosed a compact, diode-pumped, solid-state laser wherein the diode pump is butt-coupled to a laser gain material which absorbs 63% of the optical pumping radiation within a pathlength of less than 500 microns. In such a device, a divergent beam of optical pumping radiation from the diode pump is directed into a volume of the gain medium which has a sufficiently small transverse cross-sectional area so as to support only single transverse mode laser operation. Optical lenses are not needed for coupling.
J. J. Zayhowski and A. Mooradian, "Single-frequency Microship Nd Lasers," Optics Letters, Vol. 14, No. 1, (Jan. 1, 1989) pp. 24-26, have reported the construction of single-frequency microchip lasers which have a miniature, monolithic, flat-flat, solid-state cavity (e.g., 730 micron long cavity) whose mode spacing is greater than the gain bandwidth of the gain medium, and which are longitudinally pumped with the close-coupled, unfocused output of a laser diode.
The conversion of optical radiation at one frequency into optical radiation of another frequency by interaction with a non-linear optical material within an optical cavity is disclosed in U.S. Pat. No. 4,933,947 to D. W. Anthon and D. L. Sipes, "Frequency Conversion of Optical Radiation," which is assigned to the assignee of the present invention. A diode-pumped laser having a harmonic generator is disclosed by Robert Byer, G. J. Dixon and T. J. Kane in U.S. Pat. No. 4,739,507 and in an article by Byer, "Diode Laser-Pumped Solid-State Lasers," Science, Vol. 239, (Feb. 1, 1988) p. 745.
There are many practical applications of a method and apparatus which achieve harmonic conversion in a solid-state laser resonator, which is adopted to a wide variety of NLO materials, which have the advantages of small size, efficient lasing in a close-coupled pump geometry and ease of assembly, and which produce SHG outputs which are substantially greater than what might be expected from the physical size of the NLO material. Such a microlaser will not only have wide applications in the production of visible light, but also will be easy to manufacture on a mass production scale, thereby lowering costs and leading to even more practical uses.